I’m allergic to my cats, but I made a choice as an adult to balance Another (Easily Mitigable*) Allergy against having cats of my own. To whom I’m definitely less allergic... Your DD is a bit too wee for that sort of decision; however, as PP have counselled, while you need to be prepared for it, leaping right into rehoming the cats isn’t the way to go either.
• You need to be certain the cats are, indeed, the culprits. With the rash being back, I’d take her to your local pharmacy to get their advice.
• You didn’t mention any respiratory symptoms (eg sneezing, runny nose, sinus issues, coughing &/or wheezing) or eye irritation which - hopefully happily - make me think it’s more likely to be a reaction to something else. Or possibly eczema that’s being irritated by something in the home. AFAIK (other than in anaphylactic & anaphylactoid reactions, which are obviously more widespread) the rash part of pet allergy reactions tends to be localised to around where there was direct contact with the allergen.
• The pharmacist will be able to advise on whether you need to book a GP appointment. If it is an allergic!rash, obviously allergy testing would be the ideal, but an NHS referral in these circs would be vanishingly unlikely. If you can afford private, look for someone who also works in the NHS & will run bloods & arrange further care as/if necessary.
• Were you staying somewhere they provided your bedding & towels last week? It’s possible her skin’s unhappy with your washing powder - or indeed other cleaning stuff you might pick up traces of.
• Were you eating differently at all while you were away? TBH, whether or not you think you were, it’s worth keeping a food diary, especially if you’re going to end up at a GP. If the change is fairly recent, it doesn’t by any chance coincide with a grown-up getting to see your DD face to face for the first time in ages & perhaps giving her treats of some kind?
• If it IS the cats, dealing with any fur that’s not attached to them is important. So brushing them regularly; vacuuming daily; & lint-rolling so you’ll literally not have a hair out of place. That’ll also help if it’s dust[-mites] causing the issue. Not letting the cats sleep where she does until things are figured out, too - sorry if I’m stating the obvious, am just thinking if between us all we’ve given you a list of LITERALLY all the things then you’ll know you’ve really tried it all.
• Again, sorry for the obvious, but making sure your DD’s toiletries aren’t the issue. Were you using all the same ones while you were away? Superdrug’s baby toiletries include an oaty lotion/moisturiser: oats are brilliant for soothing grumpy skin. Aveeno do a whole oat range (but they’re not cruelty free if that matters to you). Child’s Farm baby range includes oaty bubble bath & their moisturisers are basically the stuff of legend. Soothing irritated skin while you uncover the cause of it is always good - & no need to start coating the wee dote in an emollient or anything.
Am sure I’ve forgotten something - had to keep stopping & coming back to this over actual hours, so just hope it makes some kind of sense at this point tbh!
*in my case - compared to anaphylaxis or just one of my “Can’t Believe It’s Not A Second Degree Burn” skin-nonsenses, cat!reaction every time please...